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How many interger between 100 -200 which is division by 9 |
| Answer» Numbers between 100 – 200 divisible by 9 are 108, 117, 126, … 198.Here, a= 108, d = 117 – 108 = 9 and an\xa0= 198.⇒ a + (n – 1)d = 198 [{tex}\\because{/tex}an\xa0= a + (n – 1)d]⇒ 108 + (n – 1)9 =198.{tex}\\implies108+9n-9=198\\\\{\\implies9n+99=198}\\\\{\\implies }{9(n+11)=198}{/tex}⇒ 11 + n =\xa0{tex}\\frac { 198 } { 9 }{/tex}⇒ n = 22 – 11.⇒ n = 11Now, S\xadn\xa0=\xa0{tex}\\frac { n } { 2 }{/tex}\xa0[2a+ (n – 1)d]⇒ S11\xa0=\xa0{tex}\\frac { 11 } { 2 }{/tex}\xa0[2(108) + (11 – 1) (9)]=\xa0{tex}\\frac { 11 } { 2 }{/tex}\xa0[216 + 99 – 9]=\xa0{tex}\\frac { 11 } { 2 }{/tex}\xa0[216 + 90]=\xa0{tex} \\frac { 11 } { 2 }{/tex}\xa0× 306= 11 × 153⇒ S11\xa0= 1683. | |